Number Theory, Analysis and Geometry
Number Theory, Analysis and Geometry
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数论、分析和几何
DOI：
10.1007/978-1-4614-1260-1_16
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发表时间：
2012
期刊：
影响因子：
--
通讯作者：
Kim M
中科院分区：
文献类型：
--
作者：
Kim M
在一封信中从Grothendieck到Faltings，有人建议，一个积极的回答thesection problem应意味着有限的点双曲曲线上的一些领域。本文指出椭圆曲线的Tate-Shafarevich群的截口猜想与有限性猜想之间的相似性。也就是说，截面猜想应该提供一个终止算法，用于找到配备有有理点的双曲曲线上的所有有理点。
In a letter from Grothendieck to Faltings, it was suggested that a positive answer to thesection conjectureshould imply finiteness of points on hyperbolic curves over number fields. In this paper, we point out instead the analogy between the section conjecture and the finiteness conjecture for the Tate-Shafarevich group of elliptic curves. That is, the section conjecture should provide a terminating algorithm for finding all rational points on a hyperbolic curve equipped with a rational point.